Instantaneous bit rate of drilling meters



p 1954 A. LUBINSKI INSTANTANEOUS BIT RATE OF DRILLING METERS 3 Sheets-Sheet 1 Filed Jan. 3, 1949 INVENTOR p 14, W54 A. LUBINSKI 2,688,871

INSTANTANEOUS BIT RATE OF DRILLING METERS Filed Jan. 3, 1949 3 Sheets-Sheet 2 INVEN TOR Sept. M, 1954 A. LLIJBINSKI 2,638,871

INSTANTANEOUS BIT RATE OF DRILLING METERS Filed Jan. 3, 1949 5 Sheets-Sheet 3 IN V EN TORv Patented Sept. 14, 1954 UNITED srAr INSTANTANEOUS BIT RATE OF DRILLING METERS 7 Claims. 1

The present invention relates to animprove- 'ment in instrumentation to be used in connection with drilling of oil wells. More particularly, it relates to an instrument for indicating the rate with which the drill bit progresses into the formation.

It is believed that no such instrument exists at present. The conventional rate of drilling instruments do not provide a measurement indicating the progress of the bit. They measure merely the progress of the downward motion of the upper extremity of the drill string commonly designated as kelly. However, the drilling string is continuously subjectedto variation of length due to elastic deformations and, therefore, the motion of the kelly is not the same as the motion of the bit. In order to eliminate the errors due to the fact that no allowance was made for the elastic variations of the length of the drill pipe, the rate of drilling determination made in the prior art consisted in measurement of the average value of the drilling rate over an appreciable depth, such as two feet for instance.

The object of this invention consists in producing a permanent indication of the instantaneous bit rate of drilling similar to an automobile speedometer, i. e. determining at any moment the rate of downward motion of the bit itself.

The details of the invention can be understood from the appended specification and the enclosed drawings in which:

Fig. la and Fig. It) show schematically certain factors affecting the operation of the proposed device at two succeeding times.

Fig. 2 shows the details of the rate indicating instrument in conjunction with conventional drilling equipment. The instrument is of the electrical type and comprises a derivator circuit as one of its elements.

Fig. 2a shows a modified weight responsive element which constitutes one of the elements of the arrangement of Fig. 2.

Fig. 3 shows another embodiment of the rate indicating instrument in conjunction with conventional drilling equipment. The instrument is of hydraulic'type.

Fig. 4 is a modification of a rate indicating instrument of electrical type in which the use of derivator circuit such as shown in Fig. 2 has been eliminated.

The principle of operation of the invention can be readily visualized from inspection of Figs.

1a, lb showing, respectively, the positions of the drilling string at an instant To and at a suitable later instant T+AT. In both figures the numeral ll designates the bore hole in process of being drilled. The drill string comprises a drill pipe section l5 extending from the top of the drill bit IS.

The drill string is subjected during the drilling process to variable tension and therefore its length varies. Of particular interest to the driller are two portions of the drill stem thatare represented by points A and B. The point A is located on the top of the drill stem directly above the earth surface. The motion of the point A is directly observable by the driller and can be indicated by means of a suitable arrangement. The point B is located at the lower extremity of the drill string at the bottom of the bore hole. The distance between A and B designated by D represents the length of the drill stem and because of the elasticity of the drill pipe the length D usually undergoes variations caused by variation of corresponding forces.

The object of the invention consists in producing an indication of the rate of progress of the bit, and therefore I am particularly interested in determining the downward motion of the lower extremity of the drill represented by the point B. This point is, however, entirely inaccessible to direct observation, and the problem consists therefore in deriving from the motion of point A (directly observable) and from certain factors controlling the length of the drill string, the desired indication'of the downward progress of the point B.

Consider now an instant To+AT represented in Fig. 1b. The point A has moved downward to a position A distant from A by the amount ADA, the point B has moved downward to the position B distant from B by the amount ADB and the new length of the drill string represented by the distance A B has now increased to a value D-l-AD. From the inspection of Figs. la and 112 it is seen that the following relation holds true:

'AT AT AT .WR designate this weight. ward, the tension decreases and at a certain .critical depth it becomes equal to zero.

It is desired to produce an indication of the Value ADE/AT representing the rate of progress of the bit and it is seen that this value can be determined by separately producing signals representing values ADA/AT and AD/AT and subsequently adding these signals.

The value ADA/AT represents the downward motion of the upper extremity of the drill stem and is 'representedby "means of 'a-suitable arrangementthat shall be explained hereafter.

The signal AD/AT representing the rate of change of the length of the drill pipe can be determined by means of the following considerations:

As stated above, the drilling string consists of a relatively thin pipe section l which issiprovided at the lower extremity .bya thickpipel'l designated as drill collars which in turn are fastened at their lower end to the drill bit I B.

It is apparent to those skilled in the art that the drill string is subjected .to internal tensions (or compressions) that are not uniform throughout its length, but decrease with the depth. Thus, for instance, the upper portions of the drill string in the neighborhood of the point A are subjected to a tension substantially equal to the weight suspended from the hook i l. Let

As I progress down- This critical depth is located below the drill pipe section somewhere within the drill collars section. The section located immediately below this depth is subjected to a small compression and this compressionincreases with the depth as I approach the point B at the bottom of the hole. At this depth the compression is equal to the weight on bit. Let WB designate this weight.

It is therefore apparent the longest portion of the drill string consists of the drill pipe l5 and is subjected only to tension which causes its elastic elongation. The relatively short section of the drill collars is subjected to compression, but the corresponding elastic deformation is negligible because thethick drill collars are practically not elastic.

We can therefore consider the overall picture .by assuming that the total drill string is subjected to .an elastic elongation, and consequently the corresponding variation AD in the length of the drillstring can be represented as Consequently, the signal representing the rate of change in the length of the drill stem can be replaced by the signal representing the rate in change in the force WR, multiplied by an appropriate coefiicient.

Substituting (6) in (4) I obtain for the desired signal representing the rate of progress in the bit an expression as follows (in the limiting case for AT- 0) d-D B dDA M13 F'FW dT (7) It is apparent from the expression ('7) that .in order to producethe desired indication :representing the progress of the drill bit two 4 separate indications are required; namely, the indication i 1 dT representing the progress of the upper extremity of the drill string and the indication representing the rate of change of the weight. I may modify somewhat the problem and express the formula (8) as follows:

dDB i Consequently, as expressed by the formula (8) the desired result may be obtained by separately producing a signal representing the value 'DA corresponding to the downward displacement of the upper extremity of the drill string, and separatelyproducing another signal WR representing the weight-suspended on the hook M. These two I signals are subsequently added to form a signal (DA-I-KWR) and subsequently another signal is produced that represents the time derivative of the sum (DA+KWR). This latter gives the desired indication representing the instantaneous rate of drilling.

Consider now Fig. 2 representing a conventional rotary drilling rig. Theprincipal portion of the arrangement shown consists of a derrick I mounted on a floor 2, crown block pulleys 3, from which a conventional traveling block :4 is suspended by means of the usual wire cables'5 terminating in the hoisting or drilling line 6. The drilling line is fed from the reel 1 by releasing a conventional brake, not shown. The movement of the hoisting or drilling line 6 about the crown pulleys 3 controls the raising and lowering of traveling block 4. The hoist line B after having passed about the crown block pulleys 3 and the traveling block pulley 5 terminates by the so-called dead line 8 which is anchored to the derrick. Mounted on the derrick floor is a conventional rotary table 9 through which the usual drilling string indicated at 10 extends into the well bore H. Drilling string I0 consists of a rotary drive member or kelly 12 attached by a swivel I3 to a hook l4 suspended from traveling block 4, hollow drill pipe I5 connected by a coupling Hi to the kelly, a hollow thick drill collar section I! and a drill bit [8 attached to the lower end of the drill collars.

The rate indicating instrument comprises the following essential elements:

(1) Means for producing a signal 'DA comprised within dotted rectangle l9. An electric voltage representing the value DA is thus produced across the output terminals 20 and 2|.

(2) Means for producing a signal KWR comprised within the dotted line 22. An electric voltage representing the value KWR is thus produced across the output terminals 23 and 24.

(3) Means for adding the signals DA. and 'KWR comprised within the dotted rectangle 25. This means is provided with two pairs of input terminals designated by numerals 26, 21 and 28, 29 and one pair of output terminals 30, 3!. The input terminals are connected in a manner so as to produce across the output terminals 30 and 3! a voltage equal to the sum of the two input voltages. Since the input voltages applied across the terminals 26, 2'! and 2B, 29 are respectively DA and KWR, then the resulting voltage across the output terminals 30, 3| represent DA-I-KWR which a voltage representing the signal DA-I-KWR is applied and one pair of output terminals 33 is produced.

(5) Means comprised within the dotted rectangle 65 for damping the fluctuations due to vibrations and other reasons which frequencies are of the same order of magnitude. The means is provided with one pair of input terminals 33, 34 and one pair of output terminals 36, 31.

(6) A suitable meter 35 measuring the voltage across the terminals 66 and 61. This meter is graduated in feet per hour and continuously indicates the instantaneous rate of penetration of the drilling bit into the formation.

The means (1), (2), (4), and (5) are described as follows:

(1) The means for producing the signal DA (within the dotted rectangle 59) comprises a pulley 36 driven by the hoist line 6 which in turn drives a worm gearing reduction 37 which moves the moving arm 38 of a potentiometer. The potentiometer comprises a semi-circular fixed resistor 39 having its terminals 40 and M supplied by a suitable battery 42. The arm 38 is provided at its extremity with a contact member adapted to slide upon the resistor in accordance with the motion of the gear. The output terminals 2| and 20 are respectively connected to the terminal 43 of the resistor and the moving arm 38. It is apparent that the output voltage across the terminals 2! and 20 represents in fact the potential drop in a portion of the resistor between the terminal 40 and the sliding contact of the moving arm 38 and, furthermore, this, voltage is proportional to the total displacement of the hoist line which in turn is proportional to DA.

(2) The means for producing a signal KWR (within the dotted line 22) comprises a strain responsive element 42. This element consists of a resistor having its two ends fastened by means of appropriately insulated terminals to a frame structure 43 which is in turn clamped to the dead line 8. The dead line is subjected to a tension which is proportional to WR. This tension is transmitted to the frame structure 53 and to the strain responsive element 32 and causes a corresponding elongation of this element which in turn causes a corresponding change in the electric resistance of the element. Consequently, the resistance of the element 42 represents the tension We. The strain responsive element 42 is made to be one of the arms of a Wheatstone bridge, the remaining three arms of which consist of resistors A l, 35 and 35. The two terminals 41 and 43 of the bridge are supplied with an A.-C. voltage source 39 and the two other terminals 50 and 5! are connected to an amplifier 52, the output of which is in turn transmitted through the two transformers 53 and 54 to a two wave rectifier 55.

It is apparent that the A.-C. voltage across 6 the terminals and 5| of the Wheatstone bridge and applied to the rectifier 55 depends upon the resistance of the element 42 and, therefore, represents WR- The rectifier is of standard construction and comprises two rectifying elements 55 connected in a manner shown in the Fig. 2 to the resistor '56 and the secondary winding of the transformer 54. The transformer 53 is an auto-transformer of any commercial type such as the Varitran manufactured by General Electric. It produces a means of changing at will the ratio between the tension WR and the output voltage across the terminals 23 and 24, said output voltage representing the value KWR. Thus a suitable value may be given to the coefficient K (see Formula 8) in accordance with the elasticity of the pipe. It is well known that the elasticity of the drill pipe depends upon the type of the pipe and its length. Consequently the values of K has to be changed from time to time as the drilling progresses.

(e) The means for producing the time derivative of the signal DA-l-KWR (within the dotted rectangle 32) is adapted to perform the process of derivation electrically in such a manner that when it receives between its input terminals 30 and 3! a certain voltage it delivers across the leads 5? and 58 a voltage varying substantially as the derivative with respect to time of the input voltage. The derivator consists of a capacitor 59 inserted between the terminal 30 and the lead 57, and of the resistor 60 inserted between the terminal 3i and the lead 51.

ihe operation of the derivator can be explained mathematically as follows: Let V1(T) be the function representing the voltage applied across the input terminals 30 and 3| of the derivator, V2(T) the function representing the voltage across the leads 5'? and 58, C the capacitance of the capacitor 58, r the resistance of the resistor 33 and HT) the current flowing through the capacitor 59. Assume also that the leads 5! and 58 of the derivator have been disconnected from the tube 3! and the battery 32. Consequently, the same current 2'(T) flows through the capacitance 59 and through the resistance 60 and the following relation holds true:

By selecting the proper values of the resistance r, for example making 1' negligibly small, the term di(T) can be made negligible as compared to proximation satisfactory for practical purposes:

Multiplying both sides of the Equation 11 by CT I obtain Consequently the expression ri(T) which rep- 7.:- resents .the voltage drop across the resistor 60 across the leadsl and 58 is substantially proportional to dV (T) dT which represents the time derivative of the input voltage across the terminals 30 and 3!.

The voltage across the leads 5'! and 58 is applied to the grid of a 3 electrode tube 6|, the cathode of which is connected to the terminal 58 by means of a biasing battery 62. A suitable B battery 63 and a resistor 64 are connected in the plate circuit. The two terminals of the resistor M are connected respectively to the terminals 33 and 34. It is well known that for a suitable choice of the type of the tube Bi and batteries 62 and 63, the plate current is proportional to the grid voltage. As the plate current flows through the resistor 62 it is also proportional to the drop of voltage across this resistor, that is to say the voltage across the terminals 33 and 34.

Consequently the voltage across the output terminals 33 and 34 represents the voltage across the leads 5'1 and 58 which is suitably amplified As the voltage across the leads 5'! and 58 is substantially proportional to the time derivative of the input voltage across the terminals 30 and 3i, then the output voltage across the terminals 33 and 34 represents the instantaneous rate of progress of the drilling bit into the formation.

(5) The means for damping the fluctuations of the voltage across the terminals 33 and 34 (within the dotted rectangle 65) without interfering with a sufficiently fast response of the instrument. The means comprises any kind of low-pass filter or simply a capacitor 68 shown on Figure 2.

It is apparent that the means 1) (comprised within the dotted rectangle I9) is not always essential to the satisfactory operation of the instrument. Particularly when the formations drilled are hard and the drilling progress is too slow for the continuous feeding of the hoist line 6, the drilling is effected by the so-called drilling off method. While drilling off, the reel 1 does not rotate at all, the hoist line 6 does not move and the progress of the drill bit is determined only from the decrease of the weight on bit. When the weight on bit decreases too much, the driller feeds the hoist line 6 by releasing the brake of the reel 1 and brings the weight on bit to its desirable value. Thereafter, a new drilling off period begins; while drilling off DA is equal to zero and the formula (8) becomes QLJL dT dT dT Thus it is evident that in hard formation areas the means (1) for producing the signal DA and the means (3) for adding this signal to another one becomes useless. The means (2) for producing the signal KWR, the means (4) for producing the time derivative of KWR, the means .(5)

KWR=K 13 for damping the vibrations and the meter 35 hook I l-or below. Such is, for instance, thezcase in the Byron Jackson electronic weightlindicator. The advantageof such an arrangement is to eliminate the error due to the friction in the pulleys 3 and 4.

Means (2) may be designed as shown on Fig. 2a. There are now commercially available weight indicators with a linear scale; that is'to say, weight indicators in which equal displacements of the moving arm on different portions of the scale correspond 'to equal differences of weight. As anexample, the Cameron Iron Works weight on bit indicator type E may be quoted.

Referring to Fig. 2a, the numeral 69'designates such a weight indicator hooked on the dead line 8 or elsewhere. The moving part of the weight indicator drives a member Ill of a variable potentiometer; the stationary part of the potentiometer consists of a semi-circular resistor 10 supplied by a suitable battery 12. It is apparent that the voltage output of the potentiometer -'|I derived from the terminals 13 and 14 represents the weight WR. This voltage is applied to the variable potentiometer 15, the output of which derived from the terminals TI and, 18 represents KWR. and may be used instead of the voltage across the terminals 23 and 24 of Fig. 2.

Consider now an arrangement of Fig. 3 showing a rate indicating instrument of hydraulic type. The elements that are common to Figs. 2and. 3 are designated by the same numerals and then the explanation is not deemed necessary. The elements that are similar but of hydraulic instead of electric type are designated by the same numerals to which the letter A was added. The instrument comprises similar elements to those of Fig. 2 designated by dotted lines ISA, 22A, 2A, 32A, 65A, and the meter 35A. These elements are as follows:

The means (1) (within the dotted rectangle I9A) comprises the same elements 36 and 37 as the electric type instrument which are respectively a pulley, worm gear, and pinion. The worm gearing 3'! drives a rack 79 which moves a rod 89 and a piston 81 within a cylinder 82. Consequently the rotation of the pulley 36 drives the piston 8| in such a manner that the displacement of the piston 8! is proportional toDA. This piston displaces an incompressible fluid out of the cylinder into a pipe 83 in accordance with the variation of DA. Therefore the displacement of the fluid is equivalent to the output voltage across terminals 20 and 2| of Fig. 2.

The means (2) (within the dotted line 22A) comprises a cylinder 84 provided with an outlet pipe 85 and a piston 86 adapted to slide within the cylinder 8 3 and thus actuate the motion of the liquid between the cylinder and the pipe. A tension spring Bl is placed between the piston and. the bottom of the cylinder. The piston 86 drives a rod 88 clamped to the dead line 8, the cylinder itself being anchored to the derrick.

It is apparent that the spring 81 is subjected to the tension proportional to WR and therefore the length of spring represents the value of WR- On the other hand, this spring controls the position of the piston 86 and consequently controls also the amount of liquid within the cylinder. Therefore the arrangement as shown is adapted to displace the liquid from the cylinder 84 to the pipe 85 in response to the value of WR; Consequently the displacement of the fluid is equivalent to the output voltage across terminals 23 and 24 of the Fig. 2.

The pipes 83 and 85 are interconnected so .as

rectangle 32A is a hydraulic derivator.

to add their outputs into a pipe 89. The conwith a suitable small orifice 94. The compartment 92 is connected to the input pipe 89 and the compartment 9| is connected to a liquid reservoir 95. The tubes 96 and 91 are respectively connected to the compartments 9| and 92 in order to measure the diiference of pressure between thesetwo compartments, pressure which is equivalent to the output voltage across terminals 33 and 34 of Fig. 2.

The means (within the dotted rectangle 65A) comprises a variable small orifice for damping purpose.

A suitable meter 35A measuring the damped diiference of pressure between the compartments 9| and 92 is equivalent to the meter 35 of Fig. 2.

The principle of operation is as follows: The amount of liquid which flows from the reservoir 95 through the cylinder 90 into the pipe 89 represents D A-I-KWR and consequently the velocity of the liquid represents the instantaneous rate of progress of the bit into the formation.

The velocity of the liquid is measured by the conventional calibrated orifice 94. The drop of pressure in the orifice is measured by the meter 35A graduated in feet per hour.

It is apparent that in this arrangement as well as in the preceding arrangements, the means (1) and (3) may be eliminated and the indication of the meter 35A will then represent the value dW dT corresponding to the instantaneous rate of drilling while drilling off.

Consider now an arrangement of Fig. 4 show- 10 comprised within the dotted rectangle [93. An electric voltage representing the value of m dT is thus produced across the output terminals B and MB.

(2) Means for producing a signal dWR dT comprised within the dotted line 223. An electric voltage representing the value of dW K dT I is thus produced across the output terminals 233 ing a rate indicating instrument of electrical type m dT and

dW K dT will be directly produced and subsequently added; that is to say that this time the formula ('7) will be applied. Consequently, the rate indicating instrument shown on Fig. 4 comprises following essential elements.

(1) Means for producing a signal in dT and 24B.

(3) Means for adding the two preceding signals comprised within the dotted rectangle 25. This means is identical to the one described in'connection with Fig. 2 and consequently the voltage across the output terminals 30 and 3| represents dD dW dT +K dT (4) Means for damping all fluctuations above some frequency, comprised 'within the rectangle 65. This means is identical to the means (*5) described in connection with Fig. 2.

(5) A voltmeter (35) identical to the one described in connection with Fig. 2 graduated in feet per hour and indicating the rate of progress of the bit into the formation.

The means (1) and (2) are described as follows:

The means (1) for producing the signal (within the dotted rectangle I9B) comprises a pulley 36 driven by the hoist line 5, which in turn drives a tachometer-generator 98. The voltage across the output terminals 293 and 2 IB is proportional to the velocity of the generator which is proportional to therefore the voltage across the output terminals 20B and ZIB represent the signal dD dT The means (2) for producing the signal (within the dotted line 22B) comprises any commercially available weight indication 99 with a linear scale and which moving parts are sufficiently powerful to drive the gears and generator which will be described later on. For example, a Byron Jackson Electronic Weight Indicator is perfectly suitable. The weight indicator drives a tachometer-generator I09 through a suitable gear train llll. It is apparent that the voltage across the output terminals I02 and IE3 of the generator I00 represents the signal (1W3 dT This voltage is applied to the variable potentiometer I94. The voltage across the output terminals 233 and 24B is the output voltage of i-i1 the potentiometer I04 and represents'the signal 011%; K dT Various other alterations and changes may be made in size, form and arrangement of the details of the described apparatus without departing from the scope of the appended claims.

What is claimed anddesired to secure by Letters Patent is:

1. A device for producing a signal representing the instantaneous'rate of penetration of'a drill bit in a rotary drilling rig'comprising in combination, means for producing a signal representing the weight on said bit, and a means responsive to said signal for producing an indication representing rate of change of said signal with time, said indication representing the instantaneous rate ofpenetration of the said-drill bit.

'2. A devicefor producing asignal-representing the intantaneous rate of penetration of a drill bit in a rotary drilling rig comprising in combination,:means forproducing a signal representing the weight on said bit and a means responsive to said signal for producing another signal representing substantially the time derivative thereof, said other signal serving as an index of the instantaneous rateof penetration of the said .drillbit.

3..Apparatus for indicatingthe progress of well drilling employing :a rotary drilling string having its upper'portionabove the earths :surface and having azbit attached'to its lower portion, comprisingameans cooperating with said upper portion for producinga signal representing the 'motion of said portion, a weight indicator for producing another signal representing the weight on the "bit, a :derivator responsive to the output of said weight indicator .for producing a signal representing the derivative with respect to time of said other signal, and means for combining said first signal and said derivative representing signal :for producing a resultant indication representing the motion of the bit.

4. Apparatus'for indicating the progress of well drilling employing an "elongated rotary drilling string having its upper portion in theneighborhood of the earths surface and having a bit attached to its lower portion comprising a means cooperating with said upper portion for producing a signal representing the 'displacementof said portion, means-for-produ'cing a'signalrepresenting the weight on the bit, means for adding said two signals thereby producing a resultant signal .and a rate indicator responsive to said last means for producing" a iresuitan't' indication having magnitude representing theiraitei of variationof said.resultantssignal-wvith:respectitoitime.

5. Apparatus for indicating the :progress well drilling by means of rotary drilling rstring having a bit attached thereto comprising/means operated in conjunction with said -'drilling:string and responsive to :the operation thereof for ;producing a signal representing the downward progress of the drilling string, means :responsive to the weight on the ibit'for producing =aasignal having magnitude representing the rate .or

change of said weight=with=respectsto .timegand means for combining said signals to produce a resultant signal representing :the progress Of the well drilling. 6. A device for producing a signal representing the instantaneous rate of penetration .of aldrill bit in a rotary drilling-rig comprising'imcombination, means for producing an electrical: signal representing the weight on said *bit, andan electrical network responsive "to :said signal .for producing another signal representing" substantially the time derivative thereof, said other signal serving as an index of the-instantaneous ducing a resultant indication representing the motionof the bit.

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1,925,012 Taylor .Aug. i29',:1933 1;967,111 Black July 17,-1934 ':2,357 ,051 McLaine Aug." 29;19414 "2,365,014 Silvermanet-al. Dec.x'12,'*1944 2,390,178 Rutherford Dec. 4, ".1945 2,419,120 Clark 'Ap1'-. :15, 1-947 42,455,917 Croke' :Dec. 14,1948 2,539,758 Silverman et al. Jan.'30, 1951 

